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2 years ago

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One of the interior angles of a triangle is equal to 30°, and one of the exterior angles is equal to 40°. Find the remaining int

erior angles of this triangle.

1 answer:

irina1246 [14]2 years ago

7 0

Answer:

The remaining interior angles of this triangle are 140º and 10º

Step-by-step explanation:

The sum of the interior angles of a triangle is always 180º.

A triangle has 3 angles. In this problem, we have one of them, that i am going to call A1 = 30º.

The sum of a interior angle with it's respective exterior angle is also always 180º.

We have that one of the exterior angles is equal to 40°. So it's respective interior angle is

40º + A2 = 180º

A2 = 180º - 40º

A2 = 140º

Now we have two interior angles, and we know that the sum of the 3 interior angles is 180º. So:

A1 + A2 + A3 = 180º

A3 = 180º - A1 - A2

A3 = 180º - 30º - 140º

A3 = 180º - 170º

A3 = 10º

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The coordinates of D is (-4,-9)

Step-by-step explanation:

Given

C = (2,7)

<em>M=(-1,-1) ----- Missing part of question</em>

Required

Determine the coordinates of D

<em>Let the coordinates of D be (x₂,y₂)</em>

<em>We'll solve this question using mid point formula;</em>

<em></em> $M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ <em></em>

<em>Where</em>

$C(x_1,y_1) = (2,7)$ and $M(x,y) = (-1,-1)$

Put these values in the formula

$(-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})$

By comparison;

$-1 = \frac{2+x_2}{2}$ and $-1 = \frac{7+y_2}{2}$

$-1 = \frac{2+x_2}{2}$

Multiply both sides by 2

$-2 = 2 + x_2$

Subtract 2 from both sides

$-2 -2 = x_2$

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Multiply both sides by 2

$-2 = 7 + y_2$

Subtract 7 from both sides

$-2 - 7 = y_2$

$y_2 = -9$

<em>Hence, the coordinates of D is (-4,-9)</em>

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